Geodesic
Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 81-82

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We study the asymptotic invertibility as $n\to+\infty$ of matrices of the form $\alpha_{kj}^{(n)}=a(k/n,j/n,k-j)$ and $\beta_{kj}^{(n)}=b(k/E(n),j/E(n),k-j)$, where $a$ and $b$ are functions defined on the sets $[0,1]\times[0,1]\times\mathbb{Z}$ and $[0,+\infty)\times[0,+\infty)\times\mathbb{Z}$, respectively, $E(n)\to+\infty$, and $n/E(n)\to+\infty$. The joint asymptotic behavior of the spectrum of these matrices is analyzed.
Keywords: asymptotic invertibility, operator, spectrum.
Mots-clés : matrix 
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     author = {O. N. Zabroda and I. B. Simonenko},
     title = {Asymptotic {Invertibility} and the {Collective} {Asymptotic} {Spectral} {Behavior} of {Generalized} {One-Dimensional} {Discrete} {Convolutions}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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O. N. Zabroda; I. B. Simonenko. Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions. Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 1, pp. 81-82. http://geodesic.mathdoc.fr/item/FAA_2004_38_1_a6/